Practice portal › Dual Nature of Matter and Radiation › Einstein's Photoelectric Equation and Work Function

The photoelectric threshold wavelength for potassium, having a work function of 2 eV, is ______. (Take h = 6.6×10⁻³⁴ J s; 1 eV = 1.6×10⁻¹⁹ J; c = 3×10⁸ m s⁻¹)

Asked in GUJCET 2008 · Threshold frequency and wavelength

• (1) 1240 m
• (2) 310.7 nm
• (3) 1860 nm
• (4) 618.7 nm

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 1240 m. The number 1240 is hc expressed in eV nm, so even read as 1240 nm it would be the threshold for a 1 eV work function. A wavelength of over a kilometre is a radio wave, whose photons carry only about 10⁻⁹ eV.
• (2) No single slip gives 310.7 nm; it is about half the correct value, roughly the threshold for a 4 eV work function. Sanity check: λ₀ = (hc)/W = (1.98×10⁻²⁵)/(3.2×10⁻¹⁹) m = 618.7 nm.
• (3) No single slip gives 1860 nm -- about three times the correct wavelength, which would mean a work function of only 0.67 eV. Sanity check: λ₀ = (hc)/W = 618.7 nm.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.